Arcane Power Regeneration Guide

As an effort to help the Wizard community, I decided to do some math regarding Arcane Power Regeneration and increases to Max Arcane Power provided from some Wizard skills. In this post I am going to show how several skills compare with each other using a hypothetical scenario. First, I will provide an overview of the skills I will be comparing. Then will be some hopefully easy to follow math. Followed with conclusions.

Arcane Power Regeneration Skills:Prodigy: This passive skill unlocked at level 20 allows you to gain 4 Arcane Power any time you successfully deal damage with a signature spell.

Astral Presence: This passive skill unlocked at level 24 allows you to regain 2 additional Arcane Power per second and adds 20 to your max AP

Familiar+Arcanot: Familiar runed with Arcanot, unlocked at levels 22 and 50 respectively, allows you to regain 2 additional Arcane Power per second.

Energy Armor: Unlocked at level 28 will increase your armor but reduce your maximum Arcane power by 20. If runed with Energy Tap unlocked at level 48 it will instead increase your Arcane Power by 20.

Time for some math!First things first, we need to establish a scenario. Our goal is to gain the most Arcane Power in 10 minutes. After learning how much Arcane Power we gain over 10 minutes we want to find out how much was usable, so for the sake of simplicity we are going to see how many Arcane Orbs runed with Tap the Source can be cast at 20 Arcane Power each. For the sake of the scenario we are using a 1.4 weapon speed wand and a 1.00 weapon speed staff. We will turn all of the regeneration statistics into what percentage of attacks you are increased over the Base. Effectively converting Arcane Power regeneration into a percent damage increase statistic based on standing and casting as long as we stay within our maximum range for weapon speed. Using our upper limits we will figure out how many signature spells vs. Arcane Orbs are cast and calculate an optimal conditions percent of total weapon damage.

Now for the somewhat tricky math. For skills like Prodigy and Magic Missile (Attunement), we only want to cast our signature spells to help with regeneration of Arcane Power. So we will only cast Magic Missile if that .7 second or 1 second cast time will not allow our Arcane Power to cap. So we need some additional Base calculations.

Using Prodigy or Attunement:Wand:.7 seconds /1 attack = 4 AP + 7 AP = 11 AP/ 1 attack/.7 secondsDivide by .7 and multiply by 10 to get = approx 15.71 AP/secondWe find the most efficient method of casting would be to cast: 10 orbs, 9 MM, then 9 orbs, 8 MM four times, followed by 9 orbs and 9 MM bringing your AP total back up to 100. This sequence takes 73.5 seconds. Over the 73.5 seconds 38.5 seconds of your time is spent casting Arcane Orb and 35 seconds are spent casting Magic Missile. This can be extrapolated to percentages.

We find the most efficient method of casting would be to cast: 10 Arcane Orbs, followed by the repeating pattern of 6 Magic Missiles and 9 Arcane Orbs. This pattern is repeated 56.48 times over 593 seconds. Over the 600 seconds 362.824 seconds of your time is spent casting Arcane Orb and 237.216 seconds are spent casting Magic Missile. This can be extrapolated to percentages.

Energy Armor and Energy Armor (Energy Tap):This skill only effects maximum Arcane Power so there is minimal impact on damage in a long term scenario. This does however affect your burst damage. With Energy tap you can get off 4 more Arcane Orbs with a staff and 3 more Arcane Orbs with a wand (at a higher rate of speed) when compared to Energy Armor without energy tap.

Familiar (Arcanot):This skill in an idea situation allows you to cast up to +19.67% more Arcane Orbs compared to the base. This accounts for a potential +3.41% damage increase with Wands and +4.54% damage increase with Staves. The benefit of this skill is that Arcane Power is regenerating passively rather than actively. So as long as you continue spending AP your AP is not wasted. This allows you to be more mobile while maintaining your damage increase of Arcane Orbs (+19.67%). We also see that staves will yield a higher benefit from this skill than wands, although higher benefit does not necessarily mean more damage.

Astral Presence: This skill in an idea situation allows you to cast up to +20% more Arcane Orbs compared to the base. This accounts for a potential +3.47% damage increase with Wands and +4.61% damage increase with Staves. The benefit of this skill is that Arcane Power is regenerating passively rather than actively. So as long as you continue spending AP your AP is not wasted. This allows you to be more mobile while maintaining your damage increase of Arcane Orbs (+20%). We also see that staves will yield a higher benefit from this skill than wands, although higher benefit does not necessarily mean more damage.

Astral Presence and Familiar (Arcanot):This skill in an idea situation allows you to cast up to +39.67% more Arcane Orbs compared to the base. This accounts for a potential +6.89% damage increase with Wands and +9.16% damage increase with Staves. The benefit of this skill is that Arcane Power is regenerating passively rather than actively. So as long as you continue spending AP your AP is not wasted. This allows you to be more mobile while maintaining your damage increase of Arcane Orbs (+39.67%). We also see that staves will yield a higher benefit from this skill than wands, although higher benefit does not necessarily mean more damage.

Prodigy or Attunement:This skill in an idea situation allows you to cast up to +47.21% more Arcane Orbs compared to the base with a Wand and 14.75% increase with Staves. This accounts for a potential +8.2% damage increase with Wands and +3.4% damage increase with Staves. The benefit of the skill is it has the potential for the most AP gain and therefore most damage. The downside is that any time AP is regenerating and you are not casting Magic Missile you waste AP, additionally if you miss a MM you waste AP. This allows for less mobility. We also see that wands will yield a higher benefit from this skill than staves by a large magin, although higher benefit does not necessarily mean more damage.

Prodigy and Attunement:This skill in an idea situation allows you to cast up to +69.83% more Arcane Orbs compared to the base with a Wand and 27.54% increase with Staves. This accounts for a potential +12.13% damage increase with Wands and +6.36% damage increase with Staves. The benefit of the skill is it has the potential for the most AP gain and therefore most damage. The downside is that any time AP is regenerating and you are not casting Magic Missile you waste AP, additionally if you miss a MM you waste AP. This allows for less mobility. We also see that wands will yield a higher benefit from this skill than staves by a large magin, although higher benefit does not necessarily mean more damage.

Comparing Passive Arcane Power Regen vs. Active Arcane Power Regen:All of the skills have their benefits but in scenarios where movement is required passive regen will mean less "wasted" Arcane Power generation. As we see with the passive regeneration skills, a X% increase in Arcane Orbs is directly equal to the increase in potential damage solely from Arcane Orb. For prodigy and attunement, this is not the case. The potential percentages of AP spenders are based on the amount of time you can cast your generator spell. The benefits and draw back here is that any time you are able to stand still and cast you will output more damage. But if you are required to move and cast your damage will be lessened.

Continued Calculations:*It has come to light that if using a stutter step method you can actually increase casting speed by a significant amount as well as allowing movement between casts. Making Prodigy and Attunement much more enticing.

The Power Hungry passive can be substantial for Arcane Power recovery, especially if you've got a decent amount of pickup radius or mobile melee teammates who just happen to pick up globes as an auxiliary effect of their attack patterns. (so that more globes are grabbed during combat rather than afterwards in which case the Power Hungry AP gain is redundant with regeneration)

Unfortunately it would be a pain to formulate, due to the many situational factors that would need to be considered and health globe drop rate potentially being a variable across acts/difficulty. But perhaps it's worth mentioning regardless.

I could do a calculation for electrocute. But I want to wait until release rather than make the calculation on speculation if the bounces would proc prodigy extra times.

The way I read it is Prodigy would generate 4 AP regardless of how many enemies the spell hits, if this is true then there is no need to do the calculation because it will have the same effectiveness as MM with Prodigy. The difference lies with the Surge of Power rune. But it is still less effective than the Attunement rune ranging from 1-3 AP per hit. Surge of Power is even less effective than Astral Presence or Familiar (Arcanot) if you hit only 1 monster.

@scape: Power hungry would be a great thing to calculate. But I have no idea how to do it. I bet if you were grouped with a barbarian with Pound of Flesh there would be a substantial AP boost.

Awesome calculations. Will be interesting to see how damage for wands versus staves (versus other viable 1h and 2h weapons) stack up. Anyway, it's now pretty clear how much optimal damage bonus could be expected with these skills, so thank you for putting this together so crystal clearly.

Power hungry would be a great thing to calculate. But I have no idea how to do it. I bet if you were grouped with a barbarian with Pound of Flesh there would be a substantial AP boost.

Seems like more simple math unless I'm overlooking something dumb (which I often do); the main challenge is to estimate some sort of health globe drop rate. If you want to be really accurate, you'd begin with number of kills per minute, and estimate a globe drop rate per monster loot-table look-up. Either way, let there be g average globe drops per minute.

Now we just need someone to play the game (not possible for the moment *sadface*) for a several hours on various difficulties and record the number of globe drops per monsters killed.

In the end, g' AP per 2 seconds is inline with the two passives. If you can keep up your kill rate, let's assume you find four in one minute, that's 2 AP/s for that minute, which is perfectly in line with Familiar/Arcanot or Astral Presence. However, this comes with the obvious downside that the player's AP regen will fluctuate more since it's dependent on the randomness of globe drop rate.

EDIT: Also, forgot to mention: that AP regen here is also dependent on kill rate, which is not such a bad thing. The more you're killing, the more AP you need and vice-versa.

I agree with you about the calculations you came up with for a base. But there are too many variables to come up with any sort of number I feel would be accurate or useful. There are a few inherent problems:1) Health globes are pretty difficult to determine how many will drop per minute. 2) How much AP will be "wasted" per health globe.

Wasted AP meaning, AP you do no receive because you are <30 AP from your MAX AP.

The AP "wasted" is not reliably calculated and depends on player usage it would be a difficult number to calculate. We could however, once we know health globe drop rates, figure for certain percentages of wasted AP. I'll try and put that in the guide once we can figure Globe drop rates.

Thanks for the Kudos, if you like the thread and find it useful request a sticky or rate the post! Happy Gaming

Beta,I am part of a theory crafting group for D3. I was wondering if you had an idea how to model a different question. I can't seem to private message here, so please get ahold of me on armadagaming under the same name!